Kinetic Energy
KE = ½mv² — see KE scale quadratically with velocity via a live curve and ball.
Key Notes
Kinetic energy K is the energy a body has due to its motion: K = ½mv².
Scalar quantity, always non-negative. Units: joule (J).
Depends on the reference frame — moving frame sees different v ⇒ different K.
K = p²/(2m), where p = mv. Useful when momentum is known.
Work-energy theorem: W_net = ΔK. Net work changes KE.
Translational KE (linear motion) + Rotational KE = total mechanical KE.
For relativistic speeds: K = (γ − 1)mc². Reduces to ½mv² for v ≪ c.
Energy of motion can be transferred to other forms: heat (friction), elastic PE (spring), gravitational PE (rising), light, sound.
Formulas
Linear KE
Always non-negative.
KE from momentum
Useful with conservation problems.
Work-energy theorem
Net work changes KE.
Relativistic KE
γ = 1/√(1−v²/c²).
Rotational KE
I = moment of inertia, ω = angular speed.
Important Points
KE is QUADRATIC in v: doubling v QUADRUPLES K. Tripling v ⇒ 9× K.
Frame-dependent: KE in lab frame ≠ KE in body frame (where it's zero).
KE is always ≥ 0 (it's ½mv²). PE can be negative.
Relativistic correction matters when v ≳ 0.1c. For everyday speeds (cars, planes), classical KE suffices.
Total KE of rolling body = ½Mv² + ½Iω² — translational plus rotational parts.
KE is NOT conserved in inelastic collisions — it converts to heat / deformation.
Kinetic Energy notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.